can it also mean "what day is it?"
This usually means “What date is it?”
I'm not a native English speaker, but is "how many days is it" really a correct translation? I have never heard this used by anyone.
You could say this naturally as a question when someone tells you they're going to participate in a multi day event, like a a race across the world or something
며칠 means "how many days". 무슨 날 이예요 means "what day is it?